Fits a one-altered zeta distribution based on a conditional model involving a Bernoulli distribution and a 1-truncated zeta distribution.
oazeta(lpobs1 = "logitlink", lshape = "loglink", type.fitted = c("mean", "shape", "pobs1", "onempobs1"), gshape = exp((-4:3)/4), ishape = NULL, ipobs1 = NULL, zero = NULL)
Link function for the parameter pobs1 or phi,
The response Y is one with probability pobs1, or Y has a 1-truncated zeta distribution with probability 1-pobs1. Thus 0 < pobs1 < 1, which is modelled as a function of the covariates. The one-altered zeta distribution differs from the one-inflated zeta distribution in that the former has ones coming from one source, whereas the latter has ones coming from the zeta distribution too. The one-inflated zeta distribution is implemented in the VGAM package. Some people call the one-altered zeta a hurdle model.
The input can be a matrix (multiple responses).
By default, the two linear/additive predictors
are (logit(phi), log(shape))^T.
An object of class
The object is used by modelling functions such as
fitted.values slot of the fitted object,
which should be extracted by the generic function
the mean mu (default) which is given by
mu = phi + (1- phi) A
where A is the mean of the one-truncated
type.fitted = "pobs1" then pobs1 is returned.
This family function effectively combines
one family function.
T. W. Yee
## Not run: odata <- data.frame(x2 = runif(nn <- 1000)) odata <- transform(odata, pobs1 = logitlink(-1 + 2*x2, inverse = TRUE), shape = loglink( 1 + 1*x2, inverse = TRUE)) odata <- transform(odata, y1 = roazeta(nn, shape = shape, pobs1 = pobs1), y2 = roazeta(nn, shape = shape, pobs1 = pobs1)) with(odata, table(y1)) ofit <- vglm(cbind(y1, y2) ~ x2, oazeta, data = odata, trace = TRUE) coef(ofit, matrix = TRUE) head(fitted(ofit)) head(predict(ofit)) summary(ofit) ## End(Not run)
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